Characterizing and Correcting Effective Target Shift in Online Learning

2026-05-11 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, extended

Summary

This research introduces a framework to analyze and improve online learning in non-stationary environments, particularly focusing on kernel regression. The authors derive a closed-form expression for online kernel regression, demonstrating its equivalence to offline regression with "effective target shifts"—inaccurate target outputs. Conversely, they prove that by compensating for these shifts through "target correction," online kernel-based learning can achieve the same predictive performance as its offline counterpart. They provide both a closed-form and an iterative, causal expression for this correction. Applying this framework to image classification tasks on CIFAR-10 and CORe50, the study shows that online stochastic gradient descent (SGD) with iteratively corrected targets outperforms learning with true targets in continual learning settings, even for non-linear models using an evolving empirical Neural Tangent Kernel (NTK).

Key takeaway

For Machine Learning Engineers developing online learning systems, understanding and correcting for effective target shifts is crucial. Your models can achieve better performance in non-stationary environments, such as continual learning, by training on iteratively corrected targets rather than raw ground-truth labels. This approach, even when heuristically applied to deep neural networks using evolving empirical Neural Tangent Kernels, significantly improves resistance to catastrophic forgetting and enhances overall accuracy.

Key insights

Online learning's sub-optimality stems from effective target shifts, which can be corrected to match offline performance.

Principles

• Online learning uses a directional kernel, unlike offline symmetric kernels.
• Prediction errors on new samples bias effective targets of neighbors.
• Training on corrected targets can outperform ground-truth targets.

Method

Online kernel regression is reformulated as offline regression with shifted targets. Target correction is derived by inverting this relationship, with an iterative approximation for causal, sequential application, even for non-linear models via empirical NTK.

In practice

• Apply iterative target correction to mitigate catastrophic forgetting.
• Use empirical NTK updates for non-linear network target correction.
• Consider target correction for online learning in structured distributional shifts.

Topics

• Online Learning
• Target Shift
• Target Correction
• Kernel Regression
• Neural Tangent Kernel

Code references

• google/neural-tangents

Best for: Computer Vision Engineer, AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.